Problem: Reduce to lowest terms: $- \dfrac{8}{3} \div - \dfrac{4}{7} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{4}{7}$ is $- \dfrac{7}{4}$ Therefore: $ - \dfrac{8}{3} \div - \dfrac{4}{7} = - \dfrac{8}{3} \times - \dfrac{7}{4} $ $ \phantom{- \dfrac{8}{3} \times - \dfrac{7}{4}} = \dfrac{-8 \times -7}{3 \times 4} $ $ \phantom{- \dfrac{8}{3} \times - \dfrac{7}{4}} = \dfrac{56}{12} $ The numerator and denominator have a common divisor of $4$, so we can simplify: $ \dfrac{56}{12} = \dfrac{56 \div 4}{12 \div 4} = \dfrac{14}{3} $